The computational complexity of geometric topology problems

Greg Kuperberg

Monday, September 23, 2013
4:00pm 5130 Upson Hall

Abstract:

I will survey some of the results and questions about the complexity
of geometric topology problems, specifically in the sense of complexity
classes. What is the complexity of distinguishing n-manifolds for various
n? Of distinguishing knots? Of recognizing a sphere, or the unknot? Last but not least I will discuss some of my own contributions: Unknot
and 3-sphere recognition are in coNP assuming the RIemann hypothesis;
approximating the Jones polynomial is #P-hard; and complexity results for
certain higher-dimensional problems.